Additive color printing

ABSTRACT

Methods and systems are provided for color printing onto nonwhite substrates and articles. For example, a method of color printing is provided, including printing multiple layers of ink each including a combination of a white ink and at least one color ink, and each printed layer having a ratio of white ink to color ink, wherein the ratio may be the same or may vary as a function of the number of layers and the color printed.

TECHNICAL FIELD

This disclosure relates generally to the field of color printing ontoany substrate, and more specifically to a method of color printing ontoany substrate (e.g., textiles or synthetic materials), the printedmaterial having any color or opacity, and achieving color management,color durability, and abrasion resistance through printing of multiplelayers of intermixed white and color printed material.

SUMMARY

Methods and systems are provided for color printing. The methods andsystems can be used with nonwhite substrates as well as with variouskinds of articles, such as clothing and footwear. To achieve printing tononwhite substrates, ink is applied in layers, with each layer having aratio of white ink to color ink.

In one aspect, a method of color printing includes printing at least afirst layer of ink comprising a white ink and at least one color ink,where the first layer of ink has a predetermined first ratio of whiteink to color ink. The method also includes printing at least a secondlayer of ink comprising the white ink and the at least one color ink,where the second layer of ink has a predetermined second ratio of whiteink to color ink different from the first ratio. The first ratio isgreater than the second ratio.

In another aspect, a method of color management includes printing atleast one color comprising multiple printed layers onto a substrate. Themultiple printed layers include at least a first layer of ink comprisinga white ink and at least one color ink, where the first layer of ink hasa predetermined first ratio of white ink to color ink. Also, at least asecond layer of ink includes the white ink and the at least one colorink, where the second layer of ink has a predetermined second ratio ofwhite ink to color ink different from the first ratio. The first ratiois greater than the second ratio.

In another aspect, a method of hot-melt printing includes printing amelt of an opaque material and at least one translucent pigmentedmaterial onto a substrate, where the opaque material and the at leastone translucent pigmented material are supplied from differentprintheads. The opaque material and the at least one translucentpigmented material are mixed on the substrate. The method also includesprinting at least one color comprising multiple printed layers of theopaque material and the at least one translucent pigmented material. Themultiple printed layers includes at least a first layer comprising theopaque material and the at least one translucent pigmented material. Thefirst layer has a predetermined first ratio of opaque material totranslucent pigmented material. Also, the multiple printed layersincludes at least a second layer comprising the opaque material and theat least one translucent pigmented material. The second layer has apredetermined second ratio of opaque material to translucent pigmentedmaterial different from the first ratio. The first ratio is greater thanthe second ratio.

In another aspect, a method of printing a desired color onto a nonwhitesubstrate by additive printing of intermixed translucent color ink andopaque white ink includes printing at least a first layer of ink ontothe nonwhite substrate with a first mixture of an opaque white ink andat least one substantially translucent color ink. The first layer of inkhas a predetermined first ratio of white ink to color ink being lessthan or equal to 1:1. The method also includes printing at least asecond layer of ink onto the nonwhite substrate with a second mixture ofthe opaque white ink and the at least one substantially translucentcolor ink. The second layer of ink has a predetermined second ratio ofwhite ink to color ink being less than or equal to 1:1. The first ratioand the second ratio are substantially equal. A sum of the first printedlayer and second printed layer produces the desired color beingoptically indistinguishable in the visible spectrum from the same colorprinted onto a white substrate using opaque color inks.

In another aspect, a method of color management includes printing atleast one desired color onto a nonwhite substrate by additive printingof intermixed translucent color ink and opaque white ink, where thedesired color comprises multiple printed layers. The multiple printedlayers include at least a first layer of ink with a first mixture of anopaque white ink and at least one substantially translucent color ink.The first layer of ink has a predetermined first ratio of white ink tocolor ink being less than or equal to 1:1. The multiple printed layersalso include at least a second layer of ink comprising a second mixtureof the opaque white ink and the at least one substantially translucentcolor ink. The second layer of ink has a predetermined second ratio ofwhite ink to color ink being less than or equal to 1:1. The first ratioand the second ratio are substantially equal, and a sum of the firstprinted layer and second printed layer produces the desired color beingoptically indistinguishable in the visual spectrum from the same colorprinted onto a white substrate using opaque color inks.

In another aspect, a method of hot-melt printing includes printing amelt of an opaque material and at least one translucent pigmentedmaterial onto a nonwhite substrate. The opaque material and the at leastone translucent pigmented material are supplied from differentprintheads. The opaque material and the at least one translucentpigmented material mix on the substrate. The printing further includesprinting at least one desired color comprising multiple printed layersof the opaque material and the at least one translucent pigmentedmaterial. The multiple printed layers include at least a first layerwith the opaque material and the at least one translucent pigmentedmaterial. The first layer has a predetermined first ratio of opaquematerial to translucent pigmented material being less than or equal to1:1. The multiple printed layers include at least a second layercomprising the opaque material and the at least one translucentpigmented material. The second layer has a predetermined second ratio ofopaque material to translucent pigmented material being less than orequal to 1:1. The first ratio and the second ratio are substantiallyequal, and a sum of the first printed layer and second printed layerproduces the desired color being optically indistinguishable in thevisual spectrum from the same color printed onto a white substrate usingopaque color inks.

BRIEF DESCRIPTION OF THE DRAWINGS

The accompanying drawings, which are incorporated in and constitute apart of this specification, illustrate embodiments and, together withthe description, serve to explain the features, advantages, andprinciples of the embodiments disclosed throughout this disclosure. Forillustration purposes, the following drawings may not be to scale.Moreover, like reference numerals designate corresponding partsthroughout the different views. In the drawings:

FIG. 1 shows a CMYK Venn diagram, consistent with an embodiment of thedisclosure;

FIG. 2 shows a perspective view of a portion of an ink printer havingCMYK and white printing capabilities, consistent with an embodiment ofthe disclosure;

FIG. 3 shows a perspective view of a sequence of printed layers printedvia a conventional printing technique used to print green color ink overa nonwhite substrate, along with a depiction of the printheads used forprinting each of the respective printed layers;

FIG. 4 shows a perspective view of an exemplary sequence of printedlayers printed consistent with an embodiment of the disclosure, theprinted layers producing a color-accurate green color ink over anonwhite substrate, along with a depiction of the printheads andrelative amounts of ink used for each of the respective printed layers;

FIG. 5 shows a perspective view of another exemplary sequence of printedlayers printed consistent with an embodiment of the disclosure, theprinted layers producing a color-accurate green color ink over anonwhite substrate, along with a depiction of the printheads andrelative amounts of ink used for each of the respective printed layers;

FIG. 6 shows a process for printing a selected color-accurate color ontoa nonwhite substrate over multiple printed layers, consistent with anembodiment of the disclosure;

FIG. 7 shows a part of the process of printing a selected color-accuratecolor of FIG. 6, consistent with an embodiment of the disclosure;

FIG. 8 shows a graphical representation of a calculated grading rule forprinting layers of different color intensity, consistent with anembodiment of the disclosure;

FIG. 9 shows another graphical representation of a calculated gradingrule for printing layers of different color intensity, consistent withan embodiment of the disclosure;

FIG. 10 shows a process for printing a selected color-accurate coloronto a nonwhite substrate, consistent with an embodiment of thedisclosure;

FIG. 11 shows a process for printing an exemplary color-accurate greencolor onto a nonwhite substrate, consistent with an embodiment of thedisclosure;

FIG. 12 shows a process for printing an exemplary color-accurate pinkcolor onto a nonwhite substrate, consistent with an embodiment of thedisclosure;

FIG. 13 shows a schematic view of an observer viewing an exemplarycolor-accurate color printed on a nonwhite substrate consistent with anembodiment of the disclosure, the color-accurate color appearingvisually the same to the observer as that comparatively printed using aconventional printing technique;

FIG. 14 shows a schematic view of an observer viewing an exemplarycolor-accurate color printed on a nonwhite substrate consistent with anembodiment of the disclosure, the color-accurate color appearingvisually the same to the observer as that comparatively printed using aconventional printing technique;

FIG. 15 shows a schematic view of an observer viewing an exemplarycolor-accurate color printed on a nonwhite substrate consistent with anembodiment of the disclosure as shown in FIGS. 13 and 14, thecolor-accurate color printed and shown in FIGS. 13 and 14 appearingvisually the same to the observer as that comparatively printed using aconventional printing technique;

FIG. 16 shows a schematic view of an observer viewing an exemplarycolor-accurate color printed on a nonwhite substrate and having ascratch or crack embedded therein, consistent with an embodiment of thedisclosure, the scratched color-accurate color appearing less visuallynoticeable to the observer as that of the scratched color comparativelyprinted using a conventional printing technique;

FIG. 17 shows a schematic view of an observer viewing an exemplarycolor-accurate color printed on a nonwhite substrate and having ascratch or crack embedded therein, consistent with an embodiment of thedisclosure, the scratched color-accurate color appearing less visuallynoticeable to the observer as that of the scratched color comparativelyprinted using a conventional printing technique;

FIG. 18 shows a schematic view of an observer viewing an exemplarycolor-accurate color printed on a nonwhite substrate and having ascratch or crack embedded therein, consistent with an embodiment of thedisclosure as shown in FIGS. 16 and 17, the scratched color-accuratecolor of FIGS. 16 and 17 appearing equally less visually noticeable tothe observer as that of the scratched color comparatively printed usinga conventional printing technique; and

FIG. 19 shows a perspective view of an athletic shoe having an uppercomprising a printed color-accurate color and a scratch or crackembedded therein along with a magnified view of the scratch regionshowing a low contrast region of slightly lighter color in the scratchwhen the shoe is printed consistent with an embodiment of thedisclosure, compared against a perspective view of an athletic shoehaving an upper comprising a printed color-accurate color and a scratchor crack embedded therein along with a magnified view of the scratchregion showing a high contrast region of white in the scratch when theshoe is printed using a conventional printing technique.

DETAILED DESCRIPTION

The following discussion and accompanying figures disclose methods andsystems for color printing onto any substrate (e.g., textiles orsynthetic materials), the printed material having any color or opacity,and achieving color management, color durability, and abrasionresistance through printing of multiple layers of intermixed white andcolor printed material. The disclosed methods and systems may use anysuitable 3D printing system.

As used throughout this disclosure, the terms “color-accurate color” and“color accuracy” refer to the accurate representation, simulation,depiction, proofing, viewing, or otherwise the observation of one ofmore colors printed consistent with an embodiment of the disclosure on awhite or a nonwhite substrate, such that the printed one or more colorsachieve substantially indistinguishable visible color differentiationfrom one or more colors in printed on a white substrate with the CMYKcolor model. As also used throughout this disclosure, the terms “colorprinting,” “inkjet printing,” “CMYK printing,” “CMYK inkjet printing,”and “color inkjet printing” refer to printing of an image by ejectingdroplets of one or more inks onto a substrate. Contrary to known “colorprinting,” “inkjet printing,” “CMYK printing,” “CMYK inkjet printing,”and “color inkjet printing,” however, the disclosed “color printing,”“inkjet printing,” “CMYK printing,” “CMYK inkjet printing,” and “colorinkjet printing” achieve color accuracy on a substrate of any color,whereas known printing techniques require printing onto a whitesubstrate, such as white paper, in order to achieve the same or similarcolor accuracy on the substrate. As also used throughout thisdisclosure, the term “color durability” refers to the ability of aprinted color to resist or otherwise minimize the visibility ofscratches, abrasions, or other marring or damage to the printed color.

As used throughout this disclosure, the term “substrate” refers to anymaterial on which printing consistent with the embodiments of thedisclosure may occur, for example, paper, plastic, metal, articles ofapparel, sports equipment, a textile, a natural fabric, a syntheticfabric, a knit, a woven material, a nonwoven material, a mesh, aleather, a synthetic leather, a polymer, a rubber, and a foam, or anycombination of them.

Consistent with an embodiment, an exemplary substrate may be, forexample, a fabric. As used throughout this disclosure, “fabric” may beused to refer generally to materials chosen from any textile, naturalfabric, synthetic fabric, knit, woven material, nonwoven material, mesh,leather, synthetic leather, polymers, rubbers, and foam, and may also beused to refer to any natural or synthetic fiber or material, such as,for example, cotton, wool, linen, silk, nylon, elastane (i.e., spandex),polyester, rayon, and olefins (i.e., polypropylene), and may furthercomprise combinations of any of these materials. Also as used throughoutthis disclosure, the terms “printing” or “printed,” and “depositing” or“deposited,” are each used synonymously, and are intended to refer tothe association of a material from a source of the material to areceiving surface or object.

Consistent with an embodiment, an exemplary substrate may also be, forexample, an article of apparel. As used throughout this disclosure, theterms “article of apparel” and “fabric” thus include any textile and anymaterials associated with or made from fabric, including a sock or ashirt, and may also be applied to any article of clothing, apparel, orequipment. For example, the disclosed embodiments may be applied tohats, caps, shirts, jerseys, jackets, socks, shorts, pants,undergarments, athletic support garments, gloves, wrist/arm bands,sleeves, headbands, any knit material, any woven material, any nonwovenmaterial, sports equipment, etc. Thus, as used throughout thisdisclosure, the term “article of apparel” may refer to any apparel orclothing, including hats, caps, shirts, jerseys, jackets, socks, shorts,pants, undergarments, athletic support garments, gloves, wrist or armbands, sleeves, headbands, any knit material, any woven material, anynonwoven material, etc.

In accordance with the systems and methods described throughout thisdisclosure, there is provided a method of color printing, comprising:printing at least a first layer of ink comprising a white ink and atleast one color ink, the first layer of ink having a predetermined firstratio of white ink to color ink; and printing at least a second layer ofink comprising the white ink and the at least one color ink, the secondlayer of ink having a predetermined second ratio of white ink to colorink different from the first ratio, wherein the first ratio is greaterthan the second ratio.

In accordance with the systems and methods described throughout thisdisclosure, there is also provided a method of color management,comprising: printing at least one color comprising multiple printedlayers onto a substrate, the multiple printed layers comprising: atleast a first layer of ink comprising a white ink and at least one colorink, the first layer of ink having a predetermined first ratio of whiteink to color ink; and at least a second layer of ink comprising thewhite ink and the at least one color ink, the second layer of ink havinga predetermined second ratio of white ink to color ink different fromthe first ratio, wherein the first ratio is greater than the secondratio.

In accordance with the systems and methods described throughout thisdisclosure, there is provided a method of hot-melt printing, comprising:printing a melt of an opaque material and at least one translucentpigmented material onto a substrate, the opaque material and the atleast one translucent pigmented material being supplied from differentprintheads, wherein the opaque material and the at least one translucentpigmented material mix on the substrate, the printing furthercomprising: printing at least one color comprising multiple printedlayers of the opaque material and the at least one translucent pigmentedmaterial, the multiple printed layers comprising: at least a first layercomprising the opaque material and the at least one translucentpigmented material, the first layer having a predetermined first ratioof opaque material to translucent pigmented material; and at least asecond layer comprising the opaque material and the at least onetranslucent pigmented material, the second layer having a predeterminedsecond ratio of opaque material to translucent pigmented materialdifferent from the first ratio, wherein the first ratio is greater thanthe second ratio.

In accordance with the systems and methods described throughout thisdisclosure, there is provided a method of printing a desired color ontoa nonwhite substrate by additive printing of intermixed translucentcolor ink and opaque white ink, comprising: printing at least a firstlayer of ink onto the nonwhite substrate comprising a first mixture ofan opaque white ink and at least one substantially translucent colorink, the first layer of ink having a predetermined first ratio of whiteink to color ink being less than or equal to 1:1; and printing at leasta second layer of ink onto the nonwhite substrate comprising a secondmixture of the opaque white ink and the at least one substantiallytranslucent color ink, the second layer of ink having a predeterminedsecond ratio of white ink to color ink being less than or equal to 1:1,wherein the first ratio and the second ratio are substantially equal,and wherein a sum of the first printed layer and second printed layerproduces the desired color being optically indistinguishable in thevisible spectrum from the same color printed onto a white substrateusing opaque color inks.

In accordance with the systems and methods described throughout thisdisclosure, there is also provided a method of color management,comprising: printing at least one desired color onto a nonwhitesubstrate by additive printing of intermixed translucent color ink andopaque white ink, the desired color comprising multiple printed layers,the multiple printed layers comprising: at least a first layer of inkcomprising a first mixture of an opaque white ink and at least onesubstantially translucent color ink, the first layer of ink having apredetermined first ratio of white ink to color ink being less than orequal to 1:1; and at least a second layer of ink comprising a secondmixture of the opaque white ink and the at least one substantiallytranslucent color ink, the second layer of ink having a predeterminedsecond ratio of white ink to color ink being less than or equal to 1:1,wherein the first ratio and the second ratio are substantially equal,and wherein a sum of the first printed layer and second printed layerproduces the desired color being optically indistinguishable in thevisual spectrum from the same color printed onto a white substrate usingopaque color inks.

In accordance with the systems and methods described throughout thisdisclosure, there is provided a method of hot-melt printing, comprising:printing a melt of an opaque material and at least one translucentpigmented material onto a nonwhite substrate, the opaque material andthe at least one translucent pigmented material being supplied fromdifferent printheads, wherein the opaque material and the at least onetranslucent pigmented material mix on the substrate, the printingfurther comprising: printing at least one desired color comprisingmultiple printed layers of the opaque material and the at least onetranslucent pigmented material, the multiple printed layers comprising:at least a first layer comprising the opaque material and the at leastone translucent pigmented material, the first layer having apredetermined first ratio of opaque material to translucent pigmentedmaterial being less than or equal to 1:1; and at least a second layercomprising the opaque material and the at least one translucentpigmented material, the second layer having a predetermined second ratioof opaque material to translucent pigmented material being less than orequal to 1:1, wherein the first ratio and the second ratio aresubstantially equal, and wherein a sum of the first printed layer andsecond printed layer produces the desired color being opticallyindistinguishable in the visual spectrum from the same color printedonto a white substrate using opaque color inks.

Additional features and advantages will be set forth in part in thedescription that follows, being apparent from the description or learnedby practice of embodiments. Both the foregoing description and thefollowing description are exemplary and explanatory, and are intended toprovide further explanation of the embodiments as claimed.

The CMYK color model used in inkjet printing typically relies on thepresence of a white substrate, such as a white piece of paper, toachieve accurate representation of the colors of one or more printedcolor inks. “CMYK” refers to four color inks used in color inkjetprinting: “C” for cyan, “M” for magenta, “Y” for yellow, and “K” forblack. Color inkjet printers may contain print heads, inkjet cartridges,or ink reservoirs of cyan, magenta, yellow, and black.

CMYK printing may produce or approximate essentially any color in thevisible spectrum by printing and intermixing various combinations ofcolor ink, as exemplified by the CMYK Venn diagram shown in FIG. 1.Referring to FIG. 1, cyan, magenta, and yellow inks may be intermixedduring printing to produce one or more colors of red, green, and blue asshown. Further intermixing of colors during printing may be used toproduce many more colors beyond the primary colors of red, green, andblue, or of cyan, magenta, and yellow, as shown in FIG. 1. Cyan,magenta, and yellow inks may also be intermixed to produce black. Blackproduced as shown in the CMYK Venn diagram of FIG. 1, however, mayappear visually to an observer as a lighter black instead of a very darkor true black. Therefore, CMYK printers may also contain a separatecartridge or reservoir filled with black ink for printing of a trueblack.

CMYK printed inks are generally considered subtractive in nature, inthat they essentially reduce the whiteness of an underlying whitesubstrate when viewed by reflected visible light by at least partiallymasking it with one or more layers of printed CMYK color inks. CMYK inksare also typically water-based, and intermix and dry on the surface ofthe substrate after printing.

Printing of the CMYK color inks typically requires a white substratebecause the printed inks are at least translucent, and color-accurateprinting relies on light reflected from an underlying white substratethrough the printed color inks to achieve color in the visible spectrumthat is recognizable to the human eye. Referring to FIG. 2, andconsistent with an embodiment, an inkjet printer 100 is shown comprisinginkjet cartridges 105. Cartridges 105 comprise cartridge 110 for cyan(“C”), cartridge 112 for magenta (“M”), cartridge 114 for yellow (“Y”),cartridge 116 for black (“K”), and two cartridges 118, 120 for white(“W”). While two cartridges for white are depicted in FIG. 2, consistentwith an embodiment, printer 100 may contain only one cartridge forwhite, or may contain more than one cartridge for white, as shown.Moreover, the ink contained in white cartridges 118, 120 may be anopaque ink, for reasons explained further below.

Still referring to FIG. 2, and consistent with an embodiment, cartridges105 may print droplets of ink 125 onto substrate 130. Substrate 130 maybe a piece of paper, or any other substrate, such as a textile orfabric, as described above. Ink droplets 125 may be ejected from one ormore of cartridges 105 and directed toward substrate 130 as shown by inkdroplet movement direction 135. As ink droplets 125 are printed,cartridges 105 may be moved across substrate 130 as shown by direction140, while substrate 130 may be moved perpendicular to direction 140 asshown by direction 145, both to facilitate printing. In this manner,printing of features 150, such as images, graphics, designs, and text,may be achieved on substrate 130.

Consistent with an embodiment, use of the CMYK color model and printingtechniques may be accomplished on white or on nonwhite substrates. Inorder to print color onto nonwhite substrates using a printer similar tothat shown in FIG. 2, layers printed using an existing printingtechnique 200 are shown in FIG. 3. Referring to FIG. 3, for example,layers printed using existing printing technique 200 first require thereproduction, simulation, or creation of an underlying white substratein order to achieve color accuracy in a final printed color printedthereon. FIG. 3 thus shows a perspective view of a sequence of printedlayers printed via an existing printing technique 200 used to printcolor ink over a nonwhite substrate, along with a depiction of theprintheads used for printing each of the respective printed layers.

As shown in FIG. 3, portions of multiple printed layers 205 are shown inperspective view. Layers 205 comprise six printed layers of white 210,212, 214, 216, 218, and 220. Six layers of white are shown in FIG. 3,although more or less layers of white may be printed using existingprinting technique 200. White layers 210, 212, 214, 216, 218, and 220are used to create a white substrate onto which color printing mayoccur. Color layer 222 is the final printed layer, printed over thewhite layers, and which may be any color printed according to the CMYKmodel.

Still referring to FIG. 3, a depiction of print cartridges or heads 230shows the inks used print the six layers of white 210, 212, 214, 216,218, and 220. For example, to print the six layers of white that createa white substrate via printed ink, white ink cartridges 232, 234 areused to eject droplets of white ink 236, while the remaining colorcartridges remain inactive. White ink 236 may be an opaque ink, whichwill reflect visible light impinging thereon in order to simulate awhite substrate underneath subsequently printed one or more translucentcolor inks. White ink 236 also serves to cover the regions of thenonwhite substrate on which subsequent printing of color will occur.

In addition, depiction of print cartridges or heads 240 in FIG. 3 showsthe inks used to print color layer 222 upon completion of printing thesix opaque layers of white. Color layer 222 may be formed from printinga translucent ink to enable reflection of visible light from theunderlying printed opaque white ink 236. For example, color layer 222may be a printed layer of color-accurate green, achieved by using inkprinted from cyan cartridge 242 and yellow cartridge 244 as shown inFIG. 3. Cartridges 242 and 244 are thus used to eject droplets oftranslucent cyan ink 246 and translucent yellow ink 248, while theremaining cartridges are inactive. Droplets 246 and 248 intermix uponprinting onto the uppermost white layer 220 to form, in the exampleshown in FIG. 3, a color-accurate green color in color layer 222. Thecolor-accurate green color of color layer 222 may be observed visuallyby viewing light reflected from underlying white layer 220 passingthrough layer 222 to an observer's eyes. Even though green color is usedin the example described with reference to FIG. 3, any color may beprinted using the CMYK color model or palette. Such color may then besubsequently observed, so long as a white substrate is first createdunderneath the final printed color layer.

Still referring to FIG. 3, a drawback to layers printed using existingprinting technique 200 is that it requires printing of many extra layersof ink in order to print color-accurate colors on a nonwhite substrate.For example, several layers of opaque white ink must first be printed inorder to effectively simulate a white substrate underlying asubsequently printed color layer. This technique requires more printingtime, more printed layers, and usage of a higher density and amount ofprinted ink. Moreover, if the final printed color layer is scratched,abraded, or otherwise marred or damaged, it is likely that the printedcolor would be removed in the region of the scratch, abrasion, or mar.Thus, it is likely that one or more of the underlying white layers wouldbe exposed, thereby displaying an undesirable high contrast between thefinal printed color layer and the exposed underlying white layer(s).Thus, the cost to print on a nonwhite substrate using the existingtechnique is greater and has more complications to achieving a finalprinted color-accurate color.

In contrast, and consistent with an embodiment, FIG. 4 shows aperspective view of an exemplary sequence of printed ink layers thatproduce a color-accurate color over a nonwhite substrate, along with adepiction of the printheads used for each of the respective printedlayers according to printing technique 300. As will be described withreference to FIG. 4, printing technique 300 differs from knowntechniques in that printer 100 may print white ink at the same time ascolor ink. The printed pattern of ink droplets may comprise a stochasticdot pattern, chaotic in nature, which mixes with itself either as theink is ejected onto the substrate or immediately upon printing onto thesubstrate. The printed white ink and color ink may thus intermix uponprinting onto a substrate, analogous to what the print industry mayidentify as a solid color or spot color. The intermixed and printedwhite and color inks are mixed on demand and upon printing onto asubstrate in a manner analogous to house paint, such that printingmultiple layers of this intermixed white and color inks builds upopacity over the course of multiple printed layers. This built-upopacity avoids the need to simulate or reproduce a white substrateunderneath the printed color layer, in contrast to known printingtechnique 200, and allows for printing color-accurate colors on nonwhitesubstrates with fewer printed layers and less ink used.

As shown in FIG. 4, portions of multiple printed layers 305 printedusing printer 100 are shown in perspective view. Layers 305 comprisefour layers of printed material 310, 312, 314, and 316. Four layers ofintermixed white and color inks are shown in the example of FIG. 4,although more or less layers may be printed to achieve printing of adesired color-accurate color. The desired color-accurate color forprinting will thus be built-up over the course of printing each oflayers 310, 312, 314, and 316 by decreasing the ratio of white ink tocolor ink with each successive printed layer. That is, the ratio ofwhite ink to color ink in first printed layer 310 may be high, while theratio of white ink to color ink in final printed layer 316 may be low.For example, the amount of white ink may decrease in each ofsuccessively printed layers 310, 312, 314, and 316, while the amount ofcolor ink may correspondingly increase in each of successively printedlayers 310, 312, 314, and 316. Details of printing technique 300 will befurther described below.

In contrast to existing technique 200, the final printed layer 316printed according to printing technique 300 does not have to be thefinal desired color-accurate color printed according to the CMYK model.That is, printing technique 300 does not require that the uppermostprinted layer solely be the color-accurate color as a standalone printedlayer. Rather, it is the combination of each of printed layers 310, 312,314, and 316 that, when taken together, create the color-accuracy for adesired color printed according to the CMYK model. Because each ofprinted layers 310, 312, 314, and 316 comprise intermixed translucentcolor ink and opaque white ink, the mixture of translucency and opacityof the various components of the printed layers work in concert toachieve observable color-accuracy of the final desired printed color.This may be observed when visible light passes through and reflects backfrom layers 310, 312, 314, and 316. This will be later described in moredetail with reference to FIG. 13.

Still referring to FIG. 4, a depiction of print cartridges or heads 330,340, 350, and 360 shows the inks used to respectively print theexemplary four layers of intermixed color and white inks 310, 312, 314,and 316. For example, to print an exemplary color-accurate green coloraccording to printing technique 300, first printed layer 310 may beprinted using the configuration of print heads 330. As part of printheads 330, cyan cartridge 331, yellow cartridge 333, and whitecartridges 332 and 334 may be used to eject droplets of white ink 336 aswell as droplets of cyan ink 335 and yellow ink 337. While two whitecartridges 332, 334 are depicted, there may be one or more whitecartridges in printer 100 as described above with reference to FIG. 2.In FIG. 4, white cartridges 332 and 334 are depicted qualitatively asejecting more white ink 336 than cyan cartridge 331 is ejecting of cyanink 335, and yellow cartridge 333 is ejecting of yellow ink 337. Firstlayer 310 may thus have the highest opacity of the layers printedaccording to printing technique 300 (and hence the largest amount ofprinted white ink), though it may not be completely white. In firstlayer 310, the comparatively smaller amounts of printed translucent cyanink 335 and translucent yellow ink 337 intermix with the opaque whiteink 336 to form layer 310.

Still referring to FIG. 4, second printed layer 312 may be printed usingthe configuration of print heads 340. As part of print heads 340, cyancartridge 331, yellow cartridge 333, and white cartridges 332 and 334may be used to eject droplets of white ink 346 as well as droplets ofcyan ink 345 and yellow ink 347. In FIG. 4, white cartridges 332 and 334are still depicted as qualitatively ejecting more white ink 346 thancyan cartridge 331 is ejecting of cyan ink 345, and yellow cartridge 333is ejecting of yellow ink 347. Second layer 312, however, may compriseless white ink 346 than first layer 310 comprises white ink 336. Thatis, second layer 312 contains more translucent color ink than firstlayer 310, and the opacity of first layer 310 may be greater than theopacity of second layer 312. In second layer 312, a greater amount ofprinted translucent cyan ink 345 and translucent yellow ink 347 intermixwith the opaque white ink 346, although layer 312 may still comprise amajority of white ink 346.

Still referring to FIG. 4, third printed layer 314 may be printed usingthe configuration of print heads 350. As part of print heads 350, cyancartridge 331, yellow cartridge 333, and white cartridges 332 and 334may be used to eject droplets of white ink 356 as well as droplets ofcyan ink 355 and yellow ink 357. Now, white cartridges 332 and 334 areno longer depicted as ejecting more white ink 356 than cyan cartridge331 is ejecting of cyan ink 355, and yellow cartridge 333 is ejecting ofyellow ink 357. Third layer 314, like second layer 312, may compriseless white ink 356 than second layer 312 comprises white ink 346. Thatis, third layer 314 may comprise even more color ink than second layer312, which in turn may comprise more color ink than first layer 310.Moreover, the opacity of second layer 312 printed according to printingtechnique 300 may be greater than the opacity of third layer 314. Inthird layer 314, an even greater amount of printed translucent cyan ink355 and translucent yellow ink 357 intermix with the opaque white ink356, and layer 314 thus comprises a majority of color ink.

Still referring to FIG. 4, fourth printed layer 316 may be printed usingthe configuration of print heads 360. As part of print heads 360, cyancartridge 331, yellow cartridge 333, and white cartridges 332 and 334may be used to eject droplets of white ink 366 as well as droplets ofcyan ink 365 and yellow ink 367. Now, white cartridges 332 and 334 ejectsubstantially less white ink 356 than cyan cartridge 331 is ejecting ofcyan ink 365, and yellow cartridge 333 is ejecting of yellow ink 367.Fourth layer 316 may comprise less white ink 366 than third layer 314comprises white ink 356. That is, fourth layer 316 may comprise evenmore color ink than third layer 314, which in turn may comprise morecolor ink than second layer 312, which in turn may comprise more colorink than first layer 310. Moreover, the opacity of third layer 314printed according to printing technique 300 may be greater than theopacity of fourth layer 316. In fourth layer 316, an even greater amountof printed translucent cyan ink 365 and translucent yellow ink 367intermix with the opaque white ink 366, and layer 316 thus comprises agreater majority of color ink than third layer 312.

Thus, technique 300 shown in FIG. 4 does not require printing ofseparate or underlying layers of white to simulate, reproduce, or createa white substrate via printed ink. Technique 300 shown in FIG. 4 mayproduce one or more color-accurate colors printed additively throughlayers of varying ratios of intermixed translucent color inks and opaquewhite inks. In the example shown in FIG. 4, color-accurate green colormay be produced through the printing of layers 310, 312, 314, and 316.The ratio of intermixed translucent color inks to opaque white inksshown in the layers of FIG. 4 may vary from low to high through each offour layers 310, 312, 314, and 316. Thus, reflection of visible lightmay occur through one or more of four layers 310, 312, 314, and 316,because there may be a portion of each of these layers comprising bothtranslucent and opaque characteristics. The number of printed layers andthe ratios of color to white inks therein may be calculated in order toachieve printing of desired color-accurate colors, such ascolor-accurate green used in the example of FIG. 4. The color-accurategreen color achieved through layers 310, 312, 314, and 316, for example,may be observed by viewing light reflected from one or more of thelayers and passing to an observer's eyes. Even though achievement ofcolor-accurate green color is used in the example described withreference to FIG. 4, any color or colors may be printed on a nonwhitesubstrate using the CMYK color model or palette with printing technique300. Such color may then be subsequently observed, without requiring thepresence of a white substrate underlying the printed color layers.

Thus, as described with reference to FIG. 4, and consistent with anembodiment, printing technique 300 may not require printing of manyextra layers of ink and may not require printing of white ink layers toeffect a white substrate. Printing technique 300 thus reduces printingtime, the number of printed layers, and may achieve color-accurate colorprinting using less ink than with existing technique 200. Moreover, ifthe final printed color layer is scratched, abraded, or otherwisedamaged or marred, the printed color may only be partially removed inthe region of the scratch, abrasion, or mar. Thus, even if one or moreof the underlying printed layers would be exposed, each underlying layerstill comprises a percentage of color ink and may thereby display only alow contrast between the scratched color layer and one or more layersimmediately above or below. Thus, the cost to print on a nonwhitesubstrate using the technique 300 is lower than that existing technique200, and achieves a final printed color-accurate color that exhibitsless contrast change when scratched, abraded, or otherwise damaged ormarred.

Consistent with an embodiment, FIG. 5 shows a perspective view ofanother exemplary sequence of printed ink layers that produce acolor-accurate color over a nonwhite substrate, along with a depictionof the printheads used for each of the respective printed layersaccording to printing technique 302. As will be described with referenceto FIG. 5, printing technique 302 differs from known techniques in thatprinter 100 may print white ink at the same time as color ink similar tothe embodiment described above with respect to FIG. 4. Consistent withan embodiment, the printed pattern of ink droplets printed according toprinting technique 302 may also comprise a stochastic dot pattern,chaotic in nature, which is mixed on demand, mixing with itself eitheras the ink is ejected onto the substrate or immediately upon printingonto the substrate. The printed white ink and color ink may thusintermix upon printing onto a substrate, analogous to what the printindustry may identify as a solid color or spot color. The intermixed andprinted white and color inks are mixed upon printing onto a substrate ina manner analogous to house paint, such that printing multiple layers ofthis intermixed white and color inks builds up opacity over the courseof multiple printed layers. This built-up opacity avoids the need tosimulate or reproduce a white substrate underneath the printed colorlayer, in contrast to known printing technique 200, and allows forprinting color-accurate colors on nonwhite substrates with fewer printedlayers and less ink used.

As shown in FIG. 5, portions of multiple printed layers 307 printedusing printer 100 are shown in perspective view. Layers 307 comprisefour layers of printed material 315. Four layers of intermixed white andcolor inks are shown in the example of FIG. 5, although more or lesslayers may be printed to achieve printing of a desired color-accuratecolor. The desired color-accurate color for printing will thus bebuilt-up over the course of printing each of layers 315 by repeating theprinting of a predetermined ratio of white ink to color ink in eachsuccessive printed layer. That is, the ratio of white ink to color inkin the first printed layer may be less than or equal to 1:1, and thismay be the same ratio applied to any number of successively printedlayers of multiple printed layers 307. Details of printing technique 302will be further described below.

In contrast to existing technique 200, the final printed layer 315 ofmultiple layers 307 printed according to printing technique 302 does nothave to be the final desired color-accurate color printed according tothe CMYK model. That is, printing technique 302, like printing technique300 describe with respect to FIG. 4, does not require that the uppermostprinted layer solely be the color-accurate color as a standalone printedlayer. Rather, it is the combination of each of the layers of multiplelayers 307 that, when taken together, create the color-accuracy for adesired color printed according to the CMYK model. Because each of thelayers of multiple layers 307 comprise intermixed translucent color inkand opaque white ink, the mixture of translucency and opacity of thevarious components of the printed layers work in concert to achieveobservable color-accuracy of the final desired printed color. This maybe observed visually as well as during instrument testing of printedcolors when considering visible light passing through and reflectingback from multiple layers 307. This will be later described in moredetail with reference to FIG. 14.

Still referring to FIG. 5, a depiction of print cartridges or heads 330,340, 350, and 360 shows the inks used to respectively print theexemplary four layers comprising multiple layers 307. For example, toprint an exemplary color-accurate green color according to printingtechnique 302, first printed layer 315 of multiple layers 307 may beprinted using the configuration of print heads 330. As part of printheads 330, cyan cartridge 331, yellow cartridge 333, and whitecartridges 332 and 334 may be used to eject droplets of white ink 376 aswell as droplets of cyan ink 375 and yellow ink 377. While two whitecartridges are again depicted (similar to FIG. 4), there may be one ormore white cartridges in printer 100 as described above with referenceto FIG. 2. In FIG. 5, printing technique 302 qualitatively uses morewhite ink 376 than cyan ink 375, and yellow ink 377. First printed layer315 of multiple layers 307 may thus have a ratio of white ink to colorink producing an opacity in between the opacity of layers 314 and 316shown in FIG. 4, and may not be completely white. For example, firstprinted layer 315 of multiple layers 307 may have a ratio of white inkto color ink being less than or equal to 1:1. Moreover, second, third,and fourth printed layers 315 of multiple layers 307 shown in FIG. 5 mayhave the same ratio of white ink to color ink as that of first printedlayer 315.

Thus, technique 302 shown in FIG. 5 likewise does not require printingof separate or underlying layers of white to simulate, reproduce, orcreate a white substrate via printed ink. Technique 302 shown in FIG. 5,similar to technique 300 shown in FIG. 4, may produce one or morecolor-accurate colors printed additively through layers comprising oneor more predetermined ratios of intermixed translucent color inks andopaque white inks. In the example shown in FIG. 5, color-accurate greencolor may be produced through the printing of layers 315 of multipleprinted layers 307. The ratio of intermixed translucent color inks toopaque white inks shown in the layers of FIG. 5 may thus be the sameratio in each of the layers 315 of multiple printed layers 307. Thus,reflection of visible light may occur through one or more of the fourlayers 315 shown in FIG. 5, because there may be a portion of each ofthese layers comprising both translucent and opaque characteristics. Thenumber of printed layers and the ratios of color to white inks thereinmay be calculated in order to achieve printing of desired color-accuratecolors, such as color-accurate green used in the example of FIG. 5. Thecolor-accurate green color achieved through multiple layers 307, forexample, may be observed by viewing light reflected from one or more ofthe layers and passing to an observer's eyes. Even though achievement ofcolor-accurate green color is used in the example described withreference to FIG. 5, any color or colors may be printed on a nonwhitesubstrate using the CMYK color model or palette with printing technique302. Such color may then be subsequently observed, without requiring thepresence of a white substrate underlying the printed color layers.

Thus, as described with reference to FIG. 5, and consistent with anembodiment, printing technique 302 may not require printing of manyextra layers of ink and may not require printing of white ink layers toeffect a white substrate. Printing technique 302 thus reduces printingtime, the number of printed layers, and may achieve color-accurate colorprinting using less ink than with existing technique 200. Moreover, ifthe final printed color layer is scratched, abraded, or otherwisedamaged or marred, the printed color may only be partially removed inthe region of the scratch, abrasion, or mar. Thus, even if one or moreof the underlying printed layers of multiple layers 307 would beexposed, each underlying layer 315 still comprises a percentage of colorink and may thereby display only a low contrast between the scratchedcolor layer and one or more layers immediately above or below. Thus, thecost to print on a nonwhite substrate using the technique 302 is lowerthan that existing technique 200, and achieves a final printedcolor-accurate color that exhibits less contrast change when scratched,abraded, or otherwise damaged or marred.

As shown in FIG. 6, and consistent with an embodiment, an exemplarygeneralized process 450 for printing color-accurate CMYK colors onnonwhite substrates begins with step 452. Some or all steps in process450 may be completed by a footwear, apparel, or equipment manufactureror proprietor. In other cases, some steps described below may beaccomplished by a manufacturer and other steps may be accomplished byanother party including another manufacturer, proprietor, retailer, orany other entity. In some cases, one or more of the steps may beoptional. In other cases, some steps may be completed in a differentorder. Referring to FIG. 5, in step 452, a desired translucent color (c)for printing is selected. Color (c) may be any color-accurate color thatcan be printed using the CMYK color model. In step 454, a desired numberof layers (n) for printing is selected, for printing the color-accuratecolor.

Still referring to FIG. 6, in step 456, each layer's printed color iscalculated based on the number of layers (n). In step 458, the currentlayer (m) is printed. In step 460, progress of color printing may beevaluated to verify whether printing is finished (n=m). If printing isfinished, then process 450 is complete. In step 460, if printing is notfinished, then process 450 may proceed to step 462. In step 462,printing may continue with the next layer (m=m+1) and return to step458.

As shown in FIG. 7, step 456 is explained in greater detail. In step470, the number of layers (n) and intensity of color (c) are used todetermine the color of the final layer (CF). In step 472, the remainingnumber of layers (n−1) is calculated. Then, in step 474, the colorintensity for each remaining layer is calculated as a percentage of CF.In step 476, CF and n are used to generate a color grading rule. In step478, the grading rule is used to compute each printed layer's colorintensity. Graphical examples of the grading rule are shown in FIGS. 8and 9.

Referring to FIG. 8, and consistent with an embodiment, a graphicalrepresentation of a grading rule is shown for the case when three layersmay be printed to achieve a color-accurate printed color. In thegraphical representation, the grading rule may be shown as a logarithmicfunction. The grading rule, however, may be a linear function,logarithmic function, exponential function, parabolic function, or anyother sequence or expression, depending on the desired color forprinting. Still referring to FIG. 8, each layer's color intensity may bea percentage of the desired CF, based on the number of layers printed.For example, as shown in FIG. 8, when three layers are printed, CF1 isthe percentage of color intensity for the first printed layer n=1.Similarly, CF2 is the percentage of color intensity for the secondprinted layer n=2; and CF3 is the percentage of color intensity for thethird printed layer n=3. Because multiple layers are printed, the colorintensity in each of the layers n=1, 2, 3 will be lower than the desiredCF due to the additive nature of printing a percentage of color in eachprinted layer.

Referring to FIG. 9, and consistent with an embodiment, anothergraphical representation of a grading rule is shown for the case whenfive layers may be printed to achieve a color-accurate printed color. Inthe graphical representation, the grading rule may be shown as alogarithmic function. The grading rule, however, may be a linearfunction, logarithmic function, exponential function, parabolicfunction, or any other sequence or expression, depending on the desiredcolor for printing. Still referring to FIG. 9, each layer's colorintensity may be a percentage of the desired CF, based on the number oflayers printed. For example, as shown in FIG. 9, when five layers areprinted, CF1 is the percentage of color intensity for the first printedlayer n=1. Similarly, CF2 is the percentage of color intensity for thesecond printed layer n=2; CF3 is the percentage of color intensity forthe third printed layer n=3; CF4 is the percentage of color intensityfor the fourth printed layer n=4; and CF5 is the percentage of colorintensity for the fifth printed layer n=5. Because multiple layers areprinted, the color intensity in each of the layers n=1, 2, 3, 4, 5 willbe lower than the desired CF due to the additive nature of printing apercentage of color in each printed layer. In addition, the graphicalrepresentations in FIGS. 8 and 9 show, for example, that the gradingrule curve may have a more shallow slope as the number of printed layers(n) increases. That is, each of CF1, CF2, CF3, CF4, and CF5 may be asmaller percentage of CF in the case of printing five layers, whereasCF1, CF2, and CF3 may be a larger percentage of CF in the case ofprinting only three layers.

As shown and described with reference to FIGS. 4-9, and consistent withan embodiment, CF may be a high percentage of the desired color-accuratefinal color C. For example, if n=3, then CF may be approximately 95% ofC; if n=4, then CF may be approximately 90% of C; if n=5, then CF may beapproximately 85% of C, etc. These percentages may also vary not justbased on the number of layers printed, but may also vary depending onthe selected color-accurate CMYK color for printing. For example,printing of lighter colors, such as pink (described later with referenceto FIG. 12), may call for CF to be an even higher percentage of C(pink). Conversely, for example, printing of darker colors, such as darkblue, may call for CF to be an overall lower percentage of C (darkblue). Moreover, in the case of the embodiment described above withrespect to FIG. 5, the color intensity in each of the printed layers maybe lower than the desired CF at a predetermined intermediate value beingsubstantially equal in each of the printed layers n, due to the additivenature of printing a percentage of color in each printed layer.

As shown in FIG. 10, and consistent with an embodiment, anotherexemplary generalized process 500 for printing color-accurate CMYKcolors on nonwhite substrates begins with step 505. Some or all steps inprocess 500 may be completed by a footwear, apparel, or equipmentmanufacturer or proprietor. In other cases, some steps described belowmay be accomplished by a manufacturer and other steps may beaccomplished by another party including another manufacturer,proprietor, retailer, or any other entity. In some cases, one or more ofthe steps may be optional. In other cases, some steps may be completedin a different order. Referring to FIG. 10, in step 505, a desiredtranslucent color (c) for printing is selected, along with an opaquewhite (w). Color (c) may be any color-accurate color that can be printedusing the CMYK color model. In step 510, a desired number of printlayers (n) is selected, for printing the color-accurate color.

Still referring to FIG. 10, in step 515, color management grading (CMG)is calculated, using a computer, for printed color and white inks as afunction of the number of printed layers. That is, (c+w)n, where (c,w≠0). In step 515, the calculated CMG provides that each printed layercomprises a combination of printed translucent color and opaque whiteinks, and that the ratio of color ink to white ink in each printed layermay vary as a function of the number of layers printed.

In step 520, a first layer of color ink and white ink is printedaccording to the calculated CMG, and the amount of color ink printed ismuch less than the amount of white ink printed. In step 525, a secondlayer of color ink and white ink is printed according to the calculatedCMG, and the amount of color ink printed is less than the amount ofwhite ink printed but more color is printed than that printed in step520. In step 530, a third layer of color ink and white ink is printedaccording to the calculated CMG, and the amount of color ink printed ismore than the amount of white ink printed, and more than that printed instep 525. In step 535, a fourth layer of color ink and white ink isprinted according to the calculated CMG, and the amount of color inkprinted is even more than the amount of white ink printed, as comparedto that printed in step 530. The process thus continues to step 540,where the nth layer of color and white ink may be printed according tothe calculated CMG, whereby the ratio of color ink to white ink maycontinue to increase with each successively printed layer. Thisexemplary process of printing varied ratios of white to color ink isanalogous to the depiction shown, for example, in FIG. 4. Alternatively,for the nonlimiting depiction shown, for example, in FIG. 5, the ratioof color ink to white ink may be fixed at a predetermined andsubstantially identical intermediate value for each successively printedlayer in steps 520, 525, 530, and 535.

In step 545, progress of color printing may be evaluated to verifywhether the calculated CMG as printed through the nth layer equals thedesired color-accurate CMYK color (c). If the number of printed layersof intermixed color and white ink produce a color-accurate desired CMYKcolor (c), then process 500 is complete. In step 545, if the calculatedCMG as printed through the nth layer does not equal the desiredcolor-accurate CMYK color (c), then process 500 may proceed to step 550.

In step 550, CMG may be recalculated based on the number of layersalready printed in steps 520 through 540, in order to determine thenumber of additional printed layers that may be necessary to achieve thedesired color-accurate CMYK color (c). In step 555, the (n+1)th layer ofcolor ink and white ink is printed according to the recalculated CMG,whereby the ratio of color ink to white ink continues to increase. Theprocess thus continues to step 560, where the (n+x)th layer of color andwhite ink is printed according to the recalculated CMG, whereby theratio of color ink to white ink continues to increase.

In step 565, progress of color printing may be reevaluated to verifywhether the recalculated CMG as printed through the (n+x)th layer equalsthe desired color-accurate CMYK color (c). If the number of printedlayers of intermixed color and white ink produce a color-accuratedesired CMYK color (c), then process 500 is complete. In step 565, ifthe recalculated CMG as printed through the (n+x)th layer does not equalthe desired color-accurate CMYK color (c), then process 500 may proceedback to step 550.

As shown in FIG. 11, and consistent with an embodiment, exemplaryprocess 600 is described for printing color-accurate green color onnonwhite substrates, which begins with step 605. Some or all steps inprocess 600 may be completed by a footwear, apparel, or equipmentmanufacturer or proprietor. In other cases, some steps described belowmay be accomplished by a manufacturer and other steps may beaccomplished by another party including another manufacturer,proprietor, retailer, or any other entity. In some cases, one or more ofthe steps may be optional. In other cases, some steps may be completedin a different order. Still referring to FIG. 11, in step 605, a desiredcolor-accurate green color (C-green) for printing is selected. C-greenmay be a color-accurate green that can be printed using the CMYK colormodel. In step 610, four layers of printing are selected for printingthe color-accurate C-green.

Still referring to FIG. 11, in step 615, color management grading forcolor-accurate green (CM-green) is calculated, using a computer, forprinted color and white inks as a function of four layers selected forprinting. In process 600, CM-green equals C-green. That is, the color tobe printed over the selected four layers to achieve CM-green will beindistinguishable by viewing from color-accurate green color (C-green)printed by known techniques. In step 615, the calculated CM-greenprovides that each printed layer comprises a percentage of printedtranslucent color inks and a percentage of printed opaque white inks,such that the ratio of color ink to white ink in each printed layervaries as a function of the number of layers printed.

In step 620, a first layer of ink is printed according to the calculatedCM-green, and in this example the first layer of ink printed comprises90% opaque white ink, 5% translucent cyan ink, and 5% translucent yellowink. In step 625, a second layer of ink is printed according to thecalculated CM-green, and in this example the second layer of ink printedcomprises 80% opaque white ink, 10% translucent cyan ink, and 10%translucent yellow ink. The amount of color ink printed in the secondlayer is thus greater than the amount of color ink printed in the firstlayer. In step 630, a third layer of ink is printed according to thecalculated CM-green, and in this example the third layer of ink printedcomprises 50% opaque white ink, 25% translucent cyan ink, and 25%translucent yellow ink. In step 635, a fourth layer of ink is printedaccording to the calculated CM-green, and in this example the fourthlayer of ink printed comprises 20% opaque white ink, 40% translucentcyan ink, and 40% translucent yellow ink. Alternatively, similar to thenonlimiting depiction shown, for example, in FIG. 5, the ratio of colorink to white ink may be fixed at a predetermined and substantiallyidentical intermediate value for each successively printed layer insteps 620, 625, 630, and 635. For example, each layer of printed ink mayalternatively comprise approximately 35% opaque white ink, approximately32.5% translucent cyan ink, and approximately 32.5% translucent yellowink, or another desired percentage between that of steps 630 and 635, toachieve the same C-green.

In step 640, progress of color printing the color-accurate C-green maybe evaluated to verify whether CM-green equals C-green. If CM-greenequals C-green, meaning color-accurate green is visible on the printednonwhite substrate, then process 600 is complete. In step 645, if thecalculated CM-green does not equal C-green, then process 600 may proceedto step 645.

In step 645, CM-green may be recalculated based on the four layersalready printed in steps 620 through 635, in order to determine thenumber of additional printed layers that may be necessary to achieve thedesired color-accurate C-green. In step 650, one or more additionallayers of color and white ink may be printed according to therecalculated CM-green. The process thus continues to step 655, where theprogress of color printing may be reevaluated to verify whether therecalculated CM-green equals C-green. If CM-green equals C-green,meaning color-accurate green is visible on the printed nonwhitesubstrate, then process 600 is complete. In step 655, if the calculatedCM-green does not equal C-green, then process 600 may proceed back tostep 645.

As shown in FIG. 12, and consistent with an embodiment, exemplaryprocess 700 is described for printing color-accurate pink color onnonwhite substrates, which begins with step 705. Some or all steps inprocess 700 may be completed by a footwear, apparel, or equipmentmanufacturer or proprietor. In other cases, some steps described belowmay be accomplished by a manufacturer and other steps may beaccomplished by another party including another manufacturer,proprietor, retailer, or any other entity. In some cases, one or more ofthe steps may be optional. In other cases, some steps may be completedin a different order. Still referring to FIG. 12, in step 705, a desiredcolor-accurate pink color for printing is selected for printing over thecourse of four layers of intermixed translucent color inks and opaquewhite ink onto a nonwhite substrate. The selected pink color may be acolor-accurate pink that can be printed using the CMYK color model.

Still referring to FIG. 12, in step 710, a first layer of ink is printedcomprising 95% opaque white ink and 5% translucent magenta ink. In step715, a second layer of ink is printed comprising 90% opaque white inkand 10% translucent magenta ink. In step 720, a third layer of ink isprinted comprising 85% opaque white ink and 15% translucent magenta ink.In step 725, a fourth layer of ink is printed comprising 80% opaquewhite ink and 20% translucent magenta ink.

Exemplary process 700 shown in FIG. 12 may thus be implemented based onvarying percentages of translucent magenta ink and opaque white inkthrough the course of printing four layers of ink on a nonwhitesubstrate. Consistent with an embodiment, however, more or less layersof ink may be printed to achieve any desired color-accurate color in theCMYK color model. Alternatively, for example, and similar to thenonlimiting depiction shown in FIG. 5, the ratio of color ink to whiteink may be fixed at a predetermined and substantially identicalintermediate value for each successively printed layer in steps 710,715, 720, and 725. For example, each layer of printed ink mayalternatively comprise approximately 82.5% opaque white ink andapproximately 17.5% translucent magenta ink to produce a color-accuratepink that can be printed using the CMYK color model.

Referring to FIG. 13, a printed surface printed according to one moretechniques disclosed herein may be visually inspected or instrumenttested and compared against a printed surface printed according to aknown technique, when both surfaces are printed onto nonwhitesubstrates. Consistent with an embodiment, observer 805 may observelight reflected from multiple printed layers 305 printed using printer100 shown and described with reference to FIG. 4. As shown in FIG. 4,layers 305 comprise four layers of printed material 310, 312, 314, and316. As shown in FIG. 13, portions of incoming visible spectrum light840 may pass through each of the four layers of printed material 310,312, 314, and 316, and reflect back from one or more of these layersback to observer 805. This is because each of layers 310, 312, 314, and316 comprise an intermixture of translucent cyan ink, translucent yellowink, and opaque white ink.

Consistent with an embodiment, light 840 is shown in FIG. 13 dividedinto light rays 815, 820, 825, and 830. Light ray 815 may pass throughuppermost printed layer 316 and reflect back through layer 316 toobserver 805. Light ray 820 may pass through printed layers 316 and 314and reflect back through layers 314 and 316 to observer 805. Light ray825 may pass through printed layers 316, 314, and 312 and reflect backthrough layers 312, 314, and 316 to observer 805. Finally, light ray 830may pass through printed layers 316, 314, 312, and 310 and reflect backthrough layers 310, 312, 314, and 316 to observer 805.

Because each of layers 310, 312, 314, and 316 comprise intermixedtranslucent color and opaque white inks, portions of light 840 may thuspenetrate through all four printed layers, or may penetrate only throughone or more printed layers. Thus, observer 805 will view a combinationof light rays 840 reflected from more than one of layers 305 to form theobserved color-accurate color. As also shown in FIG. 13, however, thiscontrasts with what observer 805 sees when viewing light 850 reflectedfrom white layer 220 printed according to the existing technique shownin FIG. 3.

For example, in FIG. 13, an observer 805 may also observe lightreflected from printed color layer 222 of layer 205 described withreference to known technique 200 of FIG. 3. As shown in FIG. 13,incoming visible spectrum light 850 may pass through color layer 222 oflayers 205, and reflect off of the uppermost surface of white layer 220,because color layer 222 comprises translucent cyan and yellow inks whilewhite layer 220 (and white layers 210 through 218) comprises opaque ink.That is, as described earlier with reference to the known technique ofFIG. 3, observer 805 will be effectively viewing printed color presentonly in layer 222, because printing of underlying white layers isrequired by known techniques to create an underlying white substrate forcolor-accurate printing.

Still referring to FIG. 13, and demonstrating the efficacy of thedisclosed printing techniques, observer 805 will nonetheless view eachof reflected light 850 and 840 and see the same color. In the case ofFIG. 13, drawn from the exemplary color printing techniques describedwith reference to FIG. 4 and in contrast with the known technique ofFIG. 3, observer 805 will see color-accurate green color when viewingeach of reflected light 850 and reflected light 840. That is, printingtechnique 300 described in FIG. 4 will produce color-accurate greencolor in a manner that is visually and instrument-testingindistinguishable from color-accurate green color printed with existingtechnique 200.

Referring to FIG. 14, a printed surface printed according to one moretechniques disclosed herein may be visually inspected or instrumenttested and compared against a printed surface printed according to aknown technique, when both surfaces are printed onto nonwhitesubstrates. Consistent with an embodiment, observer 805 may observelight reflected from multiple printed layers 307 printed using printer100 shown and described with reference to FIG. 5. As shown in FIG. 4,layers 307 comprise four layers of printed material 315. As shown inFIG. 14, portions of incoming visible spectrum light 940 may passthrough each of the four layers of printed material 315, and reflectback from one or more of these layers back to observer 805. This isbecause each of layers 315 comprise an intermixture of translucent cyanink, translucent yellow ink, and opaque white ink.

Consistent with an embodiment, light 940 is shown in FIG. 14 dividedinto light rays 915, 920, 925, and 930. Light ray 915 may pass throughuppermost printed layer 315 and reflect back through layer 315 toobserver 805. Light ray 920 may pass through the first and secondprinted layers 315 and reflect back through those layers to observer805. Likewise, light ray 925 may pass through the first, second, andthird printed layers 315 and reflect back through those layers, asshown, to observer 805. Finally, light ray 930 may pass through thefirst, second, third, and fourth printed layers and reflect back throughthose layers, as shown, to observer 805.

Because each of the printed layers 315 forming multiple printed layers307 may comprise a predetermined and substantially identical ratio ofintermixed translucent color and opaque white inks, as shown in FIG. 5,portions of light 940 may thus penetrate through all four printedlayers, or may penetrate only through one or more printed layers. Thus,observer 805 will view a combination of light rays 940 reflected frommore than one of layers 307 to form the observed color-accurate color.As also shown in FIG. 14, however, and similar to that shown in FIG. 13,this contrasts with what observer 805 sees when viewing light 850reflected from white layer 220 printed according to the existingtechnique shown in FIG. 3. For example, in FIG. 14 (and similar to whatis shown in FIG. 13), an observer 805 may also observe light reflectedfrom printed color layer 222 of layer 205 described with reference toknown technique 200 of FIG. 3.

Still referring to FIG. 14, and demonstrating the efficacy of thedisclosed printing techniques, observer 805 will nonetheless view eachof reflected light 850 and 940 and see the same color. That is, forexample, each of reflected light 850 and 940 will appear as the samecolor upon visual inspection and instrument testing of the printedlayers. In the case of FIG. 14, drawn from the exemplary color printingtechniques described with reference to FIG. 5 and in contrast with theknown technique of FIG. 3, observer 805 will see color-accurate greencolor when viewing each of reflected light 850 and reflected light 940.That is, printing technique 302 described in FIG. 5 will producecolor-accurate green color in a manner that is visually andinstrument-testing indistinguishable from color-accurate green colorprinted with existing technique 200.

Referring to FIG. 15, and consistent with an embodiment, observer 805may thus view each of reflected light 850, 840, and 940 and see the samecolor. In FIG. 15, drawn from the exemplary color printing techniquesdescribed with reference to FIGS. 4 and 5 and in contrast with the knowntechnique of FIG. 3, observer 805 will see color-accurate green colorwhen viewing each of reflected light 850, reflected light 840, andreflected light 940. That is, the printing techniques 300 and 302described with reference to FIGS. 4 and 5 will produce color-accurategreen color in a manner that is visually and instrument-testingindistinguishable from each other, as well as from the color-accurategreen color printed with existing technique 200.

Referring to FIG. 16, and consistent with an embodiment, furtherbenefits of the disclosed printing techniques will be discussed in thesituation where the printed color surface may be scratched, abraded, orotherwise damaged or marred. As shown in FIG. 16, a printed surfaceprinted according to one more techniques disclosed herein may bevisually inspected and compared against a printed surface printedaccording to a known technique, when both surfaces are printed ontononwhite substrates and when both surfaces contain as least one scratch,abrasion, or mar. For example, printed layers 305 may contain a scratch,abrasion, or mar 905, and printed layers 205 may likewise contain asubstantially identical scratch, abrasion, or mar 910.

Still referring to FIG. 16, and consistent with an embodiment, observer805 may observe light reflected from multiple printed layers 305 printedusing printer 100 shown and described with reference to FIG. 4. As shownin FIG. 16, portions of incoming visible spectrum light 1040 may passthrough each of the four layers of printed material 310, 312, 314, and316, and reflect back from one or more of these layers back to observer805. This is because each of layers 310, 312, 314, and 316 comprise anintermixture of translucent cyan ink, translucent yellow ink, and opaquewhite ink. Light 1040 may also pass through and be reflected from one ormore portions of crack 905.

Consistent with an embodiment, light 1040 is shown in FIG. 16 dividedinto light rays 1015, 1020, 1025, and 1030. Light ray 1015 may passthrough uppermost printed layer 316 and portion of crack 905 therein,and reflect back through layer 316 to observer 805. Light ray 1020 maypass through printed layers 316 and 314 and a portion of crack 905therein, and reflect back through layers 314 and 316 to observer 805.Light ray 1025 may pass through printed layers 316, 314, and 312, andcrack 905, and reflect back through layers 312, 314, and 316 to observer805. Finally, light ray 1030 may pass through printed layers 316, 314,312, and 310, and crack 905, and reflect back through layers 310, 312,314, and 316 to observer 805.

Because each of layers 310, 312, 314, and 316 comprise intermixedtranslucent color and opaque white inks, portions of light 1040 may thuspenetrate through all four printed layers, or may penetrate only throughone or more printed layers, regardless of the presence of crack 905.Thus, observer 805 may view a combination of light rays 1040 reflectedfrom more than one of layers 305 as well as from the region exposed bycrack 905. Thus, when viewing printed layers 305 comprising crack 905,observer 805 may observe crack 905, but crack 905 may only appear with aslightly lighter color or slightly darker color than the overallcolor-accurate color printed by layers 305. As also shown in FIG. 16,however, this contrasts with what observer 805 sees when viewing light950 reflected from white layer 220 and crack 910.

For example, in FIG. 16, an observer 805 may also observe lightreflected from printed color layer 222 of layer 205 described withreference to known technique 200 of FIG. 3. As shown in FIG. 16,portions of incoming visible spectrum light 950 may pass through colorlayer 222 of layers 205, and reflect off of the uppermost surface ofwhite layer 220 back to observer 805. This is because color layer 222comprises translucent cyan and yellow inks while white layer 220 (andwhite layers 210 through 218) comprises opaque ink. That is, asdescribed earlier with reference to FIG. 3, observer 805 will beeffectively viewing printed color present only in layer 222, becauseprinting of underlying white layers is required by known techniques tocreate an underlying white substrate for color-accurate printing. Light950, however, may also pass through and be reflected from one or moreportions of crack 910.

Still referring to FIG. 16, light 950 may pass through uppermost printedcolor layer 222 in the region of crack 910, and reflect back from one ormore of the underlying white layers 220, 218, etc. back to observer 805.In this case, light 950 may not pass back through color layer 222 in theregion of crack 910. Thus, when viewing printed layers 205 comprisingcrack 910, observer 805 may readily observe crack 910, as crack 910 mayappear white due to the reflection from one or more underlying whitelayers 220, 218, etc., without having passed back through color layer222 in the region of crack 910. Thus, crack 910 may appear in highcontrast against color layer 222 upon viewing by observer 805.

Referring to FIG. 17, and consistent with an embodiment, furtherbenefits of the disclosed printing techniques will be discussed in thesituation where the printed color surface may be scratched, abraded, orotherwise damaged or marred. As shown in FIG. 17, a printed surfaceprinted according to one more techniques disclosed herein may bevisually inspected or instrument tested and compared against a printedsurface printed according to a known technique, when both surfaces areprinted onto nonwhite substrates and when both surfaces contain as leastone scratch, abrasion, or mar. For example, printed layers 307, printedas described above with reference to technique 302 shown in FIG. 5, maycontain a scratch, abrasion, or mar 907, and printed layers 205 (assimilarly shown in FIG. 16) may likewise contain a substantiallyidentical scratch, abrasion, or mar 910.

Still referring to FIG. 17, and consistent with an embodiment, observer805 may observe light reflected from multiple printed layers 307 printedusing printer 100 shown and described with reference to FIG. 5. As shownin FIG. 17, portions of incoming visible spectrum light 1140 may passthrough each of the four layers 315 of printed material 307, and reflectback from one or more of these layers back to observer 805. This isbecause each of layers 315 comprise a substantially identicalpredetermined intermixture of translucent cyan ink, translucent yellowink, and opaque white ink. Light 1140 may also pass through and bereflected from one or more portions of crack 907.

Consistent with an embodiment, light 1140 is shown in FIG. 17 dividedinto light rays 1115, 1120, 1125, and 1130. Light ray 1115 may passthrough uppermost printed layer 315 and portion of crack 907 therein,and reflect back through uppermost printed layer 315 to observer 805.Light ray 1120 may pass through the first and second printed layers 315and a portion of crack 907 therein, and reflect back through theselayers to observer 805. Light ray 1125 may pass through the first,second, and third printed layers, and crack 907, and reflect backthrough these layers to observer 805. Finally, light ray 1130 may passthrough the first, second, third, and fourth printed layers, and crack907, and reflect back through these layers to observer 805.

Because each layer of printed material 307 may comprise a predeterminedand substantially identical ratio of intermixed translucent color andopaque white inks, portions of light 1140 may thus penetrate through allfour printed layers, or may penetrate only through one or more printedlayers, regardless of the presence of crack 907. Thus, observer 805 mayview a combination of light rays 1140 reflected from more than one ofthe layers as well as from the region exposed by crack 907. Thus, whenviewing the printed layers 307 comprising crack 907, observer 805 mayobserve crack 907, but crack 907 may only appear with a slightly lightercolor or slightly darker color than the overall color-accurate colorprinted by the combination of layers 307. As also shown in FIG. 17,however, and similar to that shown in FIG. 16, this contrasts with whatobserver 805 sees when viewing light 950 reflected from white layer 220and crack 910, where crack 910 may appear in high contrast against colorlayer 222 upon viewing by observer 805.

Referring to FIG. 18, and consistent with an embodiment, observer 805may thus view each of reflected light 1040 and 1140, and see the samecolor. In FIG. 18, drawn from the exemplary color printing techniquesdescribed with reference to FIGS. 16 and 17 (and in contrast with theknown technique of FIG. 3) observer 805 may see color-accurate greencolor when viewing each of reflected light 1040 and reflected light1140. That is, the printing techniques 300 and 302 described withreference to FIGS. 4 and 5 will produce color-accurate green color in amanner that is visually and instrument-testing indistinguishable fromeach other, even when one or more of the printed layers may be scratchedor otherwise marred by crack 905 or crack 907.

This difference may be exemplified as shown in FIG. 19. Referring toFIG. 19, and consistent with an embodiment, an athletic shoe, such assoccer shoe 1800, may comprise one or more printed regions 1805. Printedregions 1805 may be printed, for example, according to printingtechniques discussed herein with reference to any of FIGS. 4-12. In thecase of soccer shoe 1800, athletic use may impart significantwear-and-tear on the surface finish of the shoe. Such wear-and-tear maytake the form of any number of scratches, abrasions, or mars in thefinish of printed regions 1805. While such damage to the finish ofprinted regions 1805 may be undesirable, it may also be unavoidableduring the rigors of use demanded of shoe 1800. Therefore, it isdesirable to minimize the visibility of any such damage during theusable lifetime of shoe 1800. Such minimization may be achieved byimplementing the printing techniques disclosed herein.

Consistent with an embodiment, and still referring to FIG. 19, exemplarywear-and-tear is shown by scratch 1810 in shoe 1000. As shown anddescribed earlier with reference to FIGS. 16 and 17, light rays passingthrough printed regions 1805 will not result in a high contrastdifference between the printed regions 1805 and that of scratch 1810. Asdiscussed earlier, an observer may view a combination of light raysreflected from more than one of layers of printed regions 1805, as wellas from the region exposed by crack 1810. That is, because theunderlying printed layers comprise a mixture of translucent color inkand opaque white ink, color from one or more exposed underlying layerswill be visible to an observer when those one or more underlying layersare exposed by crack 1810. Thus, when viewing printed region 1805 andcrack 1810, crack 1810 may only appear with a slightly lighter color orslightly darker color than the overall color of printed regions 1805. Asalso shown in FIG. 19, however, this contrasts with what may be observedwhen viewing light reflected similarly from a shoe comprising regionsprinted according to existing techniques.

Still referring to FIG. 19, another exemplary wear-and-tear is alsoshown by scratch 1860 in soccer shoe 1850. Soccer shoe 1850 may compriseone or more printed regions 1855. Printed regions 1855 may be printed,for example, according to existing printing techniques discussed earlierwith reference to FIG. 3. As shown and described earlier with referenceto FIG. 16, light rays passing through printed regions 1855 will resultin a high contrast difference between the printed regions 1855 and thatof crack 1860. As discussed earlier, an observer may view light that haspassed through the opening exposed by crack 1860 and reflected off ofone or more of the underlying printed white layers back to the observer.The light, however, may also pass through and be reflected from one ormore portions of crack 1860. Thus, when viewing printed regions 1855 andcrack 1860, crack 1860 may appear with a high contrast differenceagainst printed regions 1855 due to the exposure of one or moreunderlying opaque white layers. As also shown in FIG. 19, crack 1860 mayappear as a white mark relative to the balance of printed regions 1855.

Consistent with an embodiment, therefore color durability may beachieved with printed colors according to the disclosed techniques. Thatis, damage due to scratching, abrasion, or otherwise marring a surfaceprinted using disclosed techniques will be less visible upon observationthat similar damage inflicted on a surface printing using existingtechniques. Color printing according to the disclosed techniques will bemore durable and damage less visible.

For example, applying the Stoll abrasion method, the color durability ofprinted layers printed according to known printing techniques may onlyachieve approximately 100 to approximately 120 revolutions of a Stollabrasion disc before the printed color becomes significantly damaged.This is because the existing printing techniques essentially have onlyone uppermost layer of printed color, layered over several layers ofprinted white. Any damage to the uppermost color layer will be morereadily apparent because underlying white layers may be exposed. Thus,color durability will be low.

In contrast, applying the Stoll abrasion method to printed layersprinted according to disclosed embodiments, may achieve approximately400 to approximately 450 revolutions of a Stoll abrasion disc before theprinted color becomes significantly damaged. This is because thedisclosed techniques have multiple layers of translucent color printedin combination with opaque white, such that color is printed throughoutall of the printed layers. Any damage to the uppermost color layer willbe less apparent because underlying printed layers also contain colorintermixed with white. Despite the possible exposure of one or more ofthese underlying layers, less noticeable variations in color may beobserved. Thus, color durability will be high.

Also consistent with an embodiment, the disclosed printing techniquesare also applicable to hot-melt printing, whereby solids are melted intoa viscous fluid and printed, e.g., an opaque polyurethane and at leastone translucent pigmented material. For example, abrasion resistance mayalso be achieved using the disclosed printing techniques in a hot-meltprinter, because printing of opaque polyurethane may be combined withtranslucent pigmented material that would mix together upon printingonto a substrate.

While various embodiments have been described, the description isintended to be exemplary, rather than limiting, and it will be apparentto those of ordinary skill in the art that many more embodiments andimplementations are possible that are within the scope of thedisclosure. It is intended that all such additional systems, methods,features and advantages be included within this description and thissummary, be within the scope of the disclosure, and be protected by thefollowing claims.

What is claimed is:
 1. A method of color printing, comprising: printingat least a first layer of ink comprising a white ink and at least onecolor ink, the first layer of ink having a predetermined first ratio ofwhite ink to color ink; printing at least a second layer of inkcomprising the white ink and the at least one color ink, the secondlayer of ink having a predetermined second ratio of white ink to colorink different from the first ratio, wherein the first ratio is greaterthan the second ratio, printing at least a third layer of ink comprisingthe white ink and the at least one color ink, the third layer of inkhaving a predetermined third ratio of white ink to color ink differentfrom the second ratio and the first ratio; printing at least a fourthlayer of ink comprising the white ink and the at least one color ink,the fourth layer of ink having a predetermined fourth ratio of white inkto color ink different from the third ratio, the second ratio, and thefirst ratio; wherein the second ratio is greater than the third ratio,and the third ratio is greater than the fourth ratio; and wherein anamount of the white ink printed in the second layer is less than anamount of the white ink printed in the first layer, wherein an amount ofthe white ink printed in the third layer is less than the amount of thewhite ink printed in the second layer, wherein an amount of the whiteink printed in the fourth layer is less than the amount of the white inkprinted in the third layer, wherein an amount of the at least one colorink printed in the second layer is greater than an amount of the atleast one color ink printed in the first layer, wherein an amount of theat least one color ink printed in the third layer is greater than theamount of the at least one color ink printed in the second layer, andwherein an amount of the at least one color ink printed in the fourthlayer is greater than the amount of the at least one color ink printedin the third layer.
 2. The method according to claim 1, wherein thewhite ink is substantially opaque and the at least one color ink issubstantially translucent.
 3. The method according to claim 1, whereinthe printed layers of ink are abrasion resistant.
 4. The methodaccording to claim 1, wherein the printed layers of ink are printed on atextile or fabric material.
 5. The method according to claim 1, whereinthe white ink and the at least one color ink intermix upon printing. 6.The method according to claim 1, wherein color accuracy is maintainedwhen printing onto nonwhite substrates.
 7. A method of color management,comprising: printing at least one color comprising multiple printedlayers onto a substrate, the multiple printed layers comprising: atleast a first layer of ink comprising a white ink and at least one colorink, the first layer of ink having a predetermined first ratio of whiteink to color ink; at least a second layer of ink comprising the whiteink and the at least one color ink, the second layer of ink having apredetermined second ratio of white ink to color ink different from thefirst ratio, wherein the first ratio is greater than the second ratio;at least a third layer of ink comprising the white ink and the at leastone color ink, the third layer of ink having a predetermined third ratioof white ink to color ink different from the second ratio and the firstratio; at least a fourth layer of ink comprising the white ink and theat least one color ink, the fourth layer of ink having a predeterminedfourth ratio of white ink to color ink different from the third ratio,the second ratio, and the first ratio, wherein the second ratio isgreater than the third ratio, and the third ratio is greater than thefourth ratio; and wherein an amount of the white ink printed in thesecond layer is less than an amount of the white ink printed in thefirst layer, wherein an amount of the white ink printed in the thirdlayer is less than the amount of the white ink printed in the secondlayer, wherein an amount of the white ink printed in the fourth layer isless than the amount of the white ink printed in the third layer,wherein an amount of the at least one color ink printed in the secondlayer is greater than an amount of the at least one color ink printed inthe first layer, wherein an amount of the at least one color ink printedin the third layer is greater than the amount of the at least one colorink printed in the second layer, and wherein an amount of the at leastone color ink printed in the fourth layer is greater than the amount ofthe at least one color ink printed in the third layer.
 8. The methodaccording to claim 7, wherein the white ink is substantially opaque andthe at least one color ink is substantially translucent.
 9. The methodaccording to claim 7, wherein the printed layers of ink are abrasionresistant.
 10. The method according to claim 7, wherein the substrate isa textile or fabric material.
 11. The method according to claim 7,wherein the white ink and the at least one color ink intermix uponprinting.
 12. The method according to claim 7, wherein color accuracy ismaintained when printing onto nonwhite substrates.
 13. A method ofhot-melt printing, comprising: printing a melt of an opaque material andat least one translucent pigmented material onto a substrate, the opaquematerial and the at least one translucent pigmented material beingsupplied from different printheads, wherein the opaque material and theat least one translucent pigmented material mix on the substrate, theprinting further comprising: printing at least one color comprisingmultiple printed layers of the opaque material and the at least onetranslucent pigmented material, the multiple printed layers comprising:at least a first layer comprising the opaque material and the at leastone translucent pigmented material, the first layer having apredetermined first ratio of opaque material to translucent pigmentedmaterial; at least a second layer comprising the opaque material and theat least one translucent pigmented material, the second layer having apredetermined second ratio of opaque material to translucent pigmentedmaterial different from the first ratio, wherein the first ratio isgreater than the second ratio; at least a third layer comprising theopaque material and the at least one translucent pigmented material, thethird layer having a predetermined third ratio of opaque material totranslucent pigmented material different from the second ratio and thefirst ratio; at least a fourth layer comprising the opaque material andthe at least one translucent pigmented material, the fourth layer havinga predetermined fourth ratio of opaque material to translucent pigmentedmaterial different from the third ratio, the second ratio, and the firstratio, wherein the second ratio is greater than the third ratio, and thethird ratio is greater than the fourth ratio; and wherein an amount ofthe opaque material printed in the second layer is less than an amountof the opaque material printed in the first layer, wherein an amount ofthe opaque material printed in the third layer is less than the amountof the opaque material printed in the second layer, wherein an amount ofthe opaque material printed in the fourth layer is less than the amountof the opaque material printed in the third layer, wherein an amount ofthe at least one translucent pigmented material printed in the secondlayer is greater than an amount of the at least one translucentpigmented material printed in the first layer, wherein an amount of theat least one translucent pigmented material printed in the third layeris greater than the amount of the at least one translucent pigmentedmaterial printed in the second layer, and wherein an amount of the atleast one translucent pigmented material printed in the fourth layer isgreater than the amount of the at least one translucent pigmentedmaterial printed in the third layer.
 14. The method according to claim13, wherein color accuracy is maintained despite at least partialabrading of the printed layers.
 15. The method according to claim 13,wherein the substrate is a textile or fabric material.
 16. The methodaccording to claim 13, wherein the printed materials are ejectedsimultaneously from different printheads.
 17. The method according toclaim 13, wherein color accuracy is maintained when printing ontononwhite substrates.
 18. The method according to claim 13, whereininfliction of scratching or abrasion substrate exposes a lighter shadeof the translucent pigmented material.
 19. The method according to claim1, wherein the substrate is chosen from a textile, a natural fabric, asynthetic fabric, a knit material, a woven material, a nonwovenmaterial, a natural fiber, a synthetic fiber, cotton, wool, linen, silk,nylon, spandex, polyester, rayon, polypropylene, a mesh, a leather, asynthetic leather, a polymer, a rubber, a foam, clothing, footwear,hats, caps, shirts, jerseys, jackets, socks, shorts, pants,undergarments, athletic support garments, gloves, wrist/arm bands,sleeves, headbands, and combinations of any of these materials.
 20. Themethod according to claim 13, wherein the printed material is chosenfrom an ink, a dye, a resin, an acrylic, a polymer, a thermoplasticmaterial, a thermosetting material, and a light-curable material.